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# On May 7, 1992, the space shuttle Endeavour was launched on mission STS-49, the purpose of which was to install a new perigee kick motor in an Intelsat communications satellite. The table gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters.(a) Use a graphing calculator or computer to find the cubic polynomial that best models the velocity of the shuttle for the time interval $t \in [0, 125]$. Then graph this polynomial.(b) Find a model for the acceleration of the shuttle and use it to estimate the maximum and minimum values of the acceleration during the first $125$ seconds.

## (a) $v(t)=0.00146137 t^{3}-0.115534 t^{2}+24.9817 t-21.2687$(b) The minimum acceleration is 21.94 $ft/ s^2$ The maximum acceleration is 64.60 $ft / s^2$

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

So in this problem We are given that this additional endeavor was on launched on May 7, 1992 for the mission STS 49. And were given a uh table of data of time and velocities in feet per second. Were asked to use a graphing calculator or computer model to model this data By a 3rd degree polynomial. So the way to do this is India's most is you go up here to the plus and do the table and when you do the table it'll open up a table like this and you enter the data into each of the cells here. From the table Down through their 010 15 2020 30: 59 60- 1 25. And then you put in the velocities into Y. one 01:85 3:19 for 47 And 7:42 13:25 14:40:41 51. Okay, once you have the data in there then to find the best cubic model because it says two. He was a 30 year degree polynomial to do this with. So in dez most you enter this, you enter Why the pool squiggle there. I called it Y one. So I would do the why. And then I'd go here to one. And if you click over here you get the little squiggle right here approximately and then put a letter and X one cubed another letter plus another letter for coefficient X one squared another letter. I used a B, C and D and E for my coefficients. And so the third term would have just X one, the first power, of course. And the last term is the constant. And when you do it will do the polynomial here, were you? That's the best fit you can see the r squared is 0.9996. So that's a very, very excellent fit to this data. And that gives us the 3rd degree polynomial for this data. Then it says use the model that we just came up with to estimate the height reached by the endeavour 125 seconds after lift off. Well, since we already have this graft in here, all we have to do is go up here and touch the graph Up until we get to 125 for the X. Were you right there, gives me 41 50 0.32. So 41 50.32 feet per second would be the estimate for this. So we had the point, We have the .125 and I could say why one there. Okay, that would be that point right there, right there, be right there on it, wasn't it? And there we go.

DM
Oklahoma State University

#### Topics

Derivatives

Differentiation

Volume

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp